Wendy,
This die is famous for requiring the user to go through a learning curve.
Lee advises putting about 35 lbs of force on the handle. Different presses have different mechanical advantages, but if yours is a Challenger press, then that number should be about right for it. To get the feel of that pressure, stand on a bathroom scale and push down until the scale shows 35 lbs less. I've done this and the scale is very shaky in its reading when I do, but I just look for the average to be about the right number. Unfortunately, to do that technique, I find some scales are hard to put where I can read them well. Having to look over my Budweiser tumor to see the scale probably doesn't help. But another way is to pull the knob off the press handle and press it down on the bathroom scale to get a feel for what 35 lbs of force is like. You could also pull the handle with a fish scale, but be aware the knob can fly off suddenly.
The object of all that trouble is to see if the specified weight is adequate to size your cases or not. Assuming not, you may need a mandrel adjustment either of your own or done by the factory. To find out, you want to try a couple of other things.
First, let's measure whether or not you may need it. Brass is slightly springy. You can figure between 1/2 and 1 thousandth of neck spring-back after squeezing the brass against the mandrel, so you want the mandrel to be that much smaller than the finished neck ID you want. The finished neck ID should probably be about -0.0020" smaller than the bullet for a fairly firm grip on it. You can tell what you are getting now by measuring the outside of the neck before seating a bullet, and then again over top of the widest part of the bullet to see how much it made the neck grow. But the bottom line is you likely need the mandrel 0.0025"-0.0030" smaller than the diameter of the bullet.
You can make a rough check with a digital caliper by zeroing it on a bullet, then measuring the mandrel where the bullet is squeezed against it. Calipers aren't very precise for an adjustment, but a difference measurement like that is generally pretty close.
If you are going to narrow the mandrel with wet/dry sandpaper, as described earlier, then you probably want to have a thimble OD micrometer with a 0.0001" resolution vernier scale, rather than a caliper. It's much easier to see and control what you are doing with one. For measuring the difference between a bullet and a mandrel, you only need an inexpensive one. Harbor Freight has one for $20 and Enco has one for about $15, though that doesn't include P&H. Either is adequate. If you aren't familiar with reading vernier scales, then the least expensive digital micrometer is about $35 from Harbor Freight. The main thing to remember about these tools is, despite their appearance, they are not C-clamps and should never be tightened hard on anything to avoid ruining them. A delicate touch is needed.
Second, as 603Country mentioned, if the brass has been reloaded several times before, the neck may be getting work-hardened from the repeated exercise. This can make it even more springy. To fix that you need to stress-relieve the neck. This is also called partial annealing, though most shooters just call it annealing, even though that's not strictly technically correct.
You want to try this out rather than go to the trouble of doing all your cases if you are not sure you need to do it. So pick just one case that is like the others you've had trouble with and has the same load history. Light a candle and, holding the case by its head, roll it back and forth between your thumb and index finger while letting the flame play over the neck and shoulder of the case. The soot will tell you if you are heating it evenly all around, which you want to.
When enough heat has got back to the head that it is starting to get too warm to hold onto, set the case down. Some folks slap it on a wet towel to cool it faster and get the soot off, but you can just leave it sitting upright to cool. The candle flame is cool enough that it eliminates any chance of overheating the neck and getting it too soft and weak. A temperature you can just hang onto is not nearly hot enough to anneal the head, which you must avoid doing, for safety reasons. It's a slow method, but a very safe one.
After annealing, try the case in the Lee die and see if it does any better than the others. If so, the others need annealing, too. They won't need it every time.